slarrb.f(3)

NAME
slarrb.f -

SYNOPSIS

  Functions/Subroutines
subroutine slarrb (N, D, LLD, IFIRST, ILAST, RTOL1, RTOL2, OFFSET, W, WGAP, WERR, WORK, IWORK, PIVMIN, SPDIAM, TWIST, INFO)
SLARRB provides limited bisection to locate eigenvalues for more accuracy.

Function/Subroutine Documentation

  subroutine slarrb (integerN, real, dimension( * )D, real, dimension( * )LLD, integerIFIRST, integerILAST, realRTOL1, realRTOL2, integerOFFSET, real, dimension( * )W, real, dimension( * )WGAP, real, dimension( * )WERR, real, dimension( * )WORK, integer, dimension( * )IWORK, realPIVMIN, realSPDIAM, integerTWIST, integerINFO)

SLARRB provides limited bisection to locate eigenvalues for more accuracy.

Purpose:

     Given the relatively robust representation(RRR) L D L^T, SLARRB
     does "limited" bisection to refine the eigenvalues of L D L^T,
     W( IFIRST-OFFSET ) through W( ILAST-OFFSET ), to more accuracy. Initial
     guesses for these eigenvalues are input in W, the corresponding estimate
     of the error in these guesses and their gaps are input in WERR
     and WGAP, respectively. During bisection, intervals
     [left, right] are maintained by storing their mid-points and
     semi-widths in the arrays W and WERR respectively.

Parameters:
    N

              N is INTEGER
              The order of the matrix.

    D

              D is REAL array, dimension (N)
              The N diagonal elements of the diagonal matrix D.

    LLD

              LLD is REAL array, dimension (N-1)
              The (N-1) elements L(i)*L(i)*D(i).

    IFIRST

              IFIRST is INTEGER
              The index of the first eigenvalue to be computed.

    ILAST

              ILAST is INTEGER
              The index of the last eigenvalue to be computed.

    RTOL1

              RTOL1 is REAL

    RTOL2

              RTOL2 is REAL
              Tolerance for the convergence of the bisection intervals.
              An interval [LEFT,RIGHT] has converged if
              RIGHT-LEFT.LT.MAX( RTOL1*GAP, RTOL2*MAX(|LEFT|,|RIGHT|) )
              where GAP is the (estimated) distance to the nearest
              eigenvalue.

    OFFSET

              OFFSET is INTEGER
              Offset for the arrays W, WGAP and WERR, i.e., the IFIRST-OFFSET
              through ILAST-OFFSET elements of these arrays are to be used.

    W

              W is REAL array, dimension (N)
              On input, W( IFIRST-OFFSET ) through W( ILAST-OFFSET ) are
              estimates of the eigenvalues of L D L^T indexed IFIRST throug
              ILAST.
              On output, these estimates are refined.

    WGAP

              WGAP is REAL array, dimension (N-1)
              On input, the (estimated) gaps between consecutive
              eigenvalues of L D L^T, i.e., WGAP(I-OFFSET) is the gap between
              eigenvalues I and I+1. Note that if IFIRST.EQ.ILAST
              then WGAP(IFIRST-OFFSET) must be set to ZERO.
              On output, these gaps are refined.

    WERR

              WERR is REAL array, dimension (N)
              On input, WERR( IFIRST-OFFSET ) through WERR( ILAST-OFFSET ) are
              the errors in the estimates of the corresponding elements in W.
              On output, these errors are refined.

    WORK

              WORK is REAL array, dimension (2*N)
              Workspace.

    IWORK

              IWORK is INTEGER array, dimension (2*N)
              Workspace.

    PIVMIN

              PIVMIN is REAL
              The minimum pivot in the Sturm sequence.

    SPDIAM

              SPDIAM is REAL
              The spectral diameter of the matrix.

    TWIST

              TWIST is INTEGER
              The twist index for the twisted factorization that is used
              for the negcount.
              TWIST = N: Compute negcount from L D L^T - LAMBDA I = L+ D+ L+^T
              TWIST = 1: Compute negcount from L D L^T - LAMBDA I = U- D- U-^T
              TWIST = R: Compute negcount from L D L^T - LAMBDA I = N(r) D(r) N(r)

    INFO

              INFO is INTEGER
              Error flag.

Author:
    Univ. of Tennessee

    Univ. of California Berkeley

    Univ. of Colorado Denver

    NAG Ltd.

Date:
    September 2012

Contributors:
    Beresford Parlett, University of California, Berkeley, USA
     Jim Demmel, University of California, Berkeley, USA
     Inderjit Dhillon, University of Texas, Austin, USA
     Osni Marques, LBNL/NERSC, USA
     Christof Voemel, University of California, Berkeley, USA

Definition at line 195 of file slarrb.f.

Author

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